Sam Truesdell (QFC Post-Doctoral Research Associate), Jim Bence (QFC Co-Director), John Syslo (QFC Post-Doctoral Research Associate), and Mark Ebener (Chippewa-Ottawa Resource Authority) recently had a paper accepted for publication in Fisheries Research for a special issue on data weighting in stock assessment models. These results have previously been shared with members of the Modeling Subcommittee for 1836 Treaty Waters, and the methodology is the basis for a planned workshop at Michigan State University in December 2016.
Integrated stock assessment models use data from multiple sources. For example, in catch-at-age models both the annual landed fish weight and the proportion of fish in each age class (measured via scientific sampling) are considered together. Catch-at-age models evaluate the trends in these data simultaneously, but some data sources are better indicators of population trajectories than others. Part of developing stock assessment models is assigning levels of certainty to each data source (i.e., a weight). This can be particularly difficult for the proportion-at-age samples (termed composition data). Common methods for assigning assessment model weights to fishery compositions typically do not account for processes often seen in the analysis of fishery data, such as that fish with similar characteristics (e.g., of similar ages) are often caught together, leading to correlations in the composition data. This means that composition data are often less informative then they appear based on the number of fish sampled and aged. This can lead to inflated composition weights that can produce biased estimates of population characteristics (such as stock size) and may lead to sub-optimal management strategies. Truesdell and co-authors survey methods for estimating the optimum weight for composition data (the effective sample size) in stock assessment models and apply them to two Great Lakes fish stocks – one in Lake Michigan and one in Lake Huron. They also introduces a new method that can account for correlations in composition data using a statistical approach.
The in-press article can be found here. The citation for the article and the abstract is below.
Truesdell, S.B., J.R. Bence, J.M. Syslo, and M.P. Ebener. In press. Estimating multinomial effective sample size in catch-at-age and catch-at-size models. Fisheries Research
Abstract.-Catch-at-age or catch-at-size stock assessment models require specification of an effective sample size (ESS) as a weighting component for multinomial composition data. ESS weights these data relative to other data that are fit, and is not an estimable parameter within a model that uses a multinomial likelihood. The ESS is typically less than the actual sample size (the number of fish) because of factors such as sampling groups of fish (clusters) that are caught together. A common approach for specifying ESS is to iteratively re-fit the model, estimating ESS after each fit so that the standardized residual variance is “correct,” until ESS converges. We survey iterative methods for determining ESS for a multinomial likelihood and apply them to two Great Lakes whitefish stocks. We also propose an extension of such methods: (the Generalized Mean Approach – GMA) for the case where ESS is based on mean age (or length) to account for correlation structures among proportions. Our extension allows for greater flexibility in the relationship between ESS and sampling intensity. Our results show that the choice of ESS estimation method can impact assessment model results. Simulations (in the absence of correlation structures) showed that all the approaches to calculating effective sample size could provide reasonable results on average, however methods that estimated annual ESS independently across years were highly imprecise. In our simulations and application, methods that did account for correlation structure in annual proportions produced lower ESS than those that did not and suggested that these methods are adjusting for a deviation from the multinomial correlation structure. We recommend using methods that adjust for correlation structures in the proportions, and either assuming a constant ESS or, when there is substantial inter-annual variation in sampling levels, assuming ESS is related to sampling intensity and using the GMA or a similar approach to estimate that relationship.